Joost Vercruysse

Joost Vercruysse

Université Libre de Bruxelles

Département de Mathématique

Bureau 2.O.8.104

Campus de la Plaine CP216

Boulevard du Triomphe

B-1050 Bruxelles - Belgium

Email: jvercruy - at - ulb.ac.be

Phone: +32-2-650.60.32

Main research interests are Algebra and Category theory.

More specifically, research topics include Hopf algebras and Hopf algebroids, Corings and Coalgebras, Hopf-Galois theory and Galois descent, non-commutative geometry and quantum groups.

**PhD students**

William Hautekiet | teaching assistant at ULB | started in October 2019

Paul Grosskopf | FRIA fellow | started in October 2020

Thomas Letourmy | teaching assistant at ULB | co-supervision with Leandro Vendramin | started in October 2021**Postdocs**Paolo Saracco | Chargé de recherche at FRNS | at ULB since May 2018

Johannes Berger | post-doctoral researcher on ARC project | at ULB since October 2021

Ryan Aziz | Marie Curie IF@ULB grant | at ULB since November 2021**Former PhD students**

Isar Goyvaerts | teaching assistant VUB | co-supervision with Stef Caenepeel (VUB) | PhD defended August 2013 | thesis title : Techniques from monoidal category theory applied to generalized Lie algebras and various types of dualities

Gabriel Kadjo | FRIA fellow | co-supervision with Marino Gran (UCL) | PhD defended September 2016 | thesis title : Semi-abelian aspects of cocommutative Hopf algebras

Jiawei Hu | CSC grant | joint PhD between East China Normal University (local supervisor Sheng-Li Tan) and ULB | PhD defended July 2018 | thesis title: Partial actions in algebraic geometry

Timmy Fieremans | teaching assistant VUB | co-supervision with Stef Caenepeel (VUB) | PhD defended September 2019 | thesis title: Hopf and Frobenius V-categories

Hoan-Phung Bui | teaching assistant ULB | co-supervision with Gabor Wiese (Université de Luxembourg) | PhD defended September 2020 | thesis title : Correspondence theorems in Hopf-Galois theory for separable field extensions

Florence Sterck | FRIA fellow | co-supervision with Marino Gran (UCL) | PhD defended September 2021 | thesis title: Split Extensions, Actions and Crossed Modules in Categories of Hopf Algebras**Former Postdocs**Mitchell Buckley | post-doctoral researcher on ARC project October 2015 - September 2016 | ULB individual fellowship December 2016 - May 2018

Dimitri Chikhladze | post-doctoral researcher on ARC project | May 2016 - September 2016

Christina Vasilakopoulou | post-doctoral researcher on ARC project | October 2016 - September 2017

Jonathan Grant | post-doctoral researcher on ARC project | October 2016 - September 2017

Réamonn O’Buachalla | post-doctoral researcher on MIS project | June 2018 - May 2020

Alessandro Iraci | post-doctoral researcher my MIS project | November 2019 - March 2020**Long term visitors**

Eliezer Batista | Universidade Federal de Santa Catarina, Florianopolis, Brazil | January 2013 - January 2014

Ana Cristina Correa Munaretto | Universidade de Paraná, Brasil | February 2014 - July 2014

Matheus Teixeira | Universidade Federal de Santa Catarina, Florianopolis, Brazil | August 2017 - March 2018

Arthur Neto | Univerisade Federal do Paraná, Brazil | December 2021 - May 2022

- As this website is determined to become outdated, more updated versions of the publication list, as well as free pdf-preprint versions of all papers can be found on arXiv, Google Scholar, Researchgate and DI-fusion.
**Preprints**P. Saracco and J. Vercruysse, Geometric partial comodules over flat coalgebras in Abelian categories are globalizable, arXiv:2107.07299

M. D'Adderio, W. Hautekiet, P. Saracco and J. Vercruysse, Partial and global representations of finite groups, arXiv:2005.09465

P. Saracco and J. Vercruysse, Globalizations of geometric partial actions, arXiv:2001.07669.**Accepted for publication/in press**

P. Saracco and J. Vercruysse, On the globalization of geometric partial (co)modules in the categories of topological spaces and algebras, arXiv:2107.06574, accepted for publication in Semigroup Forum.

A. Agore, A. Gordienko and J. Vercruysse, V-universal Hopf algebras (co)acting on Ω-algebras, arXiv:2005.12954, to appear in Communications in Contemporary Mathematics.**Published**

[33] M. Buckley, T. Fieremans, C. Vasilakopoulou, J. Vercruysse, Oplax Hopf algebras. High. Struct. 5 (2021), no. 1, 71–120.

[32] A. Agore, A. Gordienko and J. Vercruysse, Equivalences of (co)module algebra structures over Hopf algebras. J. Noncommut. Geom. 15 (2021), no. 3, 951–993.

[31] G. Böhm, J. Vercruysse, BiHom Hopf algebras viewed as Hopf monoids, Contemporary Mathematics 771 (2021), 1--41.

[30] M.M.S. Alves, E. Batista, F. Castro, G. Quadros and J. Vercruysse, Partial corepresentations of Hopf algebras, J. Algebra 577 (2021), 74–135.

[29] M. Buckley, T. Fieremans, C. Vasilakopoulou and J. Vercruysse, A Larson-Sweedler theorem for Hopf V-categories, Adv. Math. 376 (2021), 107456.

[28] J. Hu and J. Vercruysse, Geometrically partial actions, Trans. Amer. Math. Soc., 373 (2020), 4085–4143.

[27] M.M.S. Alves, E. Batista and J. Vercruysse, Dilations of partial representations of Hopf algebras, J. Lond. Math. Soc. 100 (2019), 273–300.

[26] M. Gran, F. Sterck and J. Vercruysse, A semi-abelian extension of a theorem by Takeuchi, J. Pure Appl. Algebra 223 (2019), 4171–4190.

[25] M. Gran, G. Kadjo and J. Vercruysse, Split extension classifiers in the category of cocommutative Hopf algebras, Bull. Belg. Math. Soc. Simon Stevin 25 (2018), 355–382.

[24] S. Caenepeel, E. Batista and J. Vercruysse, Hopf categories, Algebr. Represent. Theory, 19 (2016), 1173–1216.

[23] M. Gran, G. Kadjo and J. Vercruysse, A Torsion Theory in the Category of Cocommutative Hopf Algebras, Appl. Categ. Structures, 24 (2016) 269–282.

[22] E. Batista and J. Vercruysse, Dual constructions for partial actions of Hopf algebras, J. Pure Appl. Algebra 220 (2016), 518--559.

[21] M.M.S. Alves, E. Batista and J. Vercruysse, Partial representations of Hopf algebras, J. Algebra 426 (2015).

[20] I. Goyvaerts and J. Vercruysse, Lie monads and dualities, J. Algebra 414 (2014), 120--158.

[19] I. Goyvaerts and J. Vercruysse, On the duality of generalized Lie and Hopf algebras, On the duality of generalized Lie and Hopf algebras, Adv. Math. 258 (2014), 154--190.

[18] J. Vercruysse, Hopf algebras -- Variant notions and reconstruction theorems, in ``Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse'', C. Heunen, M. Sadrzadeh, E. Grefenstette (eds.). Oxford University Press, Oxford, 2013, 115--145.

[17] I. Goyvaerts and J. Vercruysse, A note on the categorisation of Lie algebras, in ``Lie Theory and its applications in physics IX'', V. Dobrev (eds.), Spring Proceedings in Mathematics and Statistics 36, Springer, Tokyo, 2013, 541--550.

[16] T. Brzezinski, A. Vazquez Marquez and J. Vercruysse, The Eilenberg-Moore category and a Beck-type theorem for a Morita context, Appl. Categorical Structures 19, (2011), 821--858.

[15] K. Janssen and J. Vercruysse, Multiplier Hopf and bi-algebras, J. Algebra Appl. 9 (2), (2010), 275 -- 303.

[14] F. Castaño Iglesias, C. Nastasescu, J. Vercruysse, Quasi-Frobenius functors. Applications, Comm Algebra, 38 (8), (2010), 3057-3077.

[13] G. Böhm and J. Vercruysse, Morita theory for comodules over corings, Comm Algebra. 37 (9), (2009), 3207 -- 3247.

[12] T. Brzezinski and J. Vercruysse, Bimodule Herds, J. Algebra, 321 (9), (2009), 2670--2704.

[11] L. El Kaoutit and J. Vercruysse, Cohomology for Bicomodules. Separable and Maschke Functors, Journal of K-theory, 3 (1) (2009), 123--152.

[10] J. Vercruysse, Quasi-co-Frobenius corings as Galois comodules, Arabian Journal for Science and Engeneering, 22 (2C) (2008), 529--552.

[9] J. Vercruysse, Equivalences between categories of Modules and categories of Comodules, Acta Math. Sin. (Engl. Ser.) 24 (10) (2008), 1655--1674.

[8] M. Iovanov and J. Vercruysse, Cofrobenius Corings and adjoint Functors, Journal of Pure and Applied Algebra, 212 (9), 2027-2058 (2008).

[7] J. Gómez-Torrecillas and J. Vercruysse, Comatrix Corings and Galois Comodules over firm rings, Algebras and Representation Theory, 10 (3) (2007), 271--306.

[6] G. Böhm and J. Vercruysse, Morita theory for Coring extensions and Cleft bicomodules, Advances in Mathematics 209 (2007), 611--648. Corrigendum, Advances in Mathematics 221 (2009), 682--686.

[5] S. Caenepeel, E. De Groot and J. Vercruysse, Galois theory for Comatrix Corings: Descent theory, Morita theory, Frobenius and separability properties, Trans. Amer. Math. Soc. 359 (2007), 185--226.

[4] S. Caenepeel, E. De Groot and J. Vercruysse, Constructing Infinite Comatrix Corings from Colimits, Appl. Categorical Structures, 14 (2006), 539--565.

[3] J. Vercruysse, Local units versus local projectivity. Dualisations : Corings with local structure maps, Communications in Algebra 34 (2006), 2079--2103.

[2] S. Caenepeel, J. Vercruysse and Shuanhong Wang, Rationality properties for Morita contexts associated to corings, in ``Hopf algebras in non-commutative geometry and physics", Caenepeel S. and Van Oystaeyen, F. (eds.), Lect. Notes Pure Appl. Math., Dekker, New York (2005) 113--136.

[1] S. Caenepeel, J. Vercruysse and Shuanhong Wang, Morita Theory for corings and cleft entwining structures, Journal of Algebra 276 (2004) 210--235.**Edited volumes**

S. Caenepeel, M. Gran, J. Vercruysse, Y. Zhang (eds.), “New trends in Hopf algebras and tensor categories”, Bull. Belgian Math. Soc. - Simon Stevin 23 (2016) issue 5, ISSN 1370-1444.

S. Caenepeel, M. Gran, J. Vercruysse, Y. Zhang (eds.), “New trends in Hopf algebras and tensor categories (Part II)”, Bull. Belgian Math. Soc. - Simon Stevin 24 (2017) issue 1, ISSN 1370-1444.

- CDR (Crédit de recherche) by FNRS | Coactions of generalized Hopf algebras (Ref. J.0061.13 CDR FRFC) | EUR 6500 | 2013-2014
- ARC consolidator grant by FWB | Hopf algebras and the symmetries of non-commutative spaces | EUR 200 000 | 2015-2018
- MIS (Incentive grant for research) by FNRS | Actions in Non-commuTatIve algebra and Partial mODulEs (ANTIPODE) | EUR 286 000 | 2018-2021
- ARC advanced grant by FWB | From algebra to combinatorics, and back | joint with Michele D'Adderio, Dimitri Leemans and Spela Spenko | EUR 663 381 | 2021-2024
- Fonds Thelam (Foundation Roi Baudeouin) | Partial Symmetries of Non-Commutative Spaces | EUR 25 000 | 2021-2024

**Future events**

Second antipode workshop | Brussels (ULB) | was planned September 2020 but postponed due to Covid-19**Past events**Hopf algebra Workshops | joint workshops by VUB and ULB | January 31, March 19 and April 17 2012

New trends in Hopf algebras and tensor categories | Brussels | June 2-5 2015

Brauer groups, Hopf algebras and monoidal categories | conference in Honour of Stef Caenepeel’s 60th birthday | Turin | May 24-27 2016

Hopf algebras @ Brussels | Brussels (ULB) | September 28-29 2016

Séminaire Itinérante de Catégories (SIC) | Brussels (ULB) | January 27 2017

Brussels Hopf algebra workshop | Brussels (ULB) | August 29-30 2017

First antipode workshop | Brussels (ULB) | 19-10 March 2018

Aspects of Higher representation theory: quantum groups and categorification | Brussels (VUB) | 21-25 January 2019

- Seminar on Quantum groups, Hopf algebras and monoidal categories | joint UCL-ULB-VUB seminar
- Category theory seminar | joint UCL-ULB-VUB seminar

Students can find info and lecture notes on each of the courses I teach via the UV-page.

**MathF102**Algèbre Linéaire et Géométrie: aspects théoriques et algorithmiques | BA Mathématique | bloc 1**MathF3003**Algèbre et géométrie II | BA Mathématique | bloc 3**MathS202**

Mathématique: algèbre linéaire II et fonctions de plusieurs de variables | BA Ingénieur de gestion | bloc 2**MathF407**Groupes, algèbres et représentations | MA Mathématique**MathF519**

Algèbre catégorique | MA Mathématique

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